Quantum Mechanics and Operator algebras on the Hilbert ball
| dc.creator | Kawamura, Katsunori | |
| dc.date | 1997-10-21 | |
| dc.date | 2007-07-24 | |
| dc.date.accessioned | 2026-07-07T08:19:46Z | |
| dc.date.available | 2026-07-07T08:19:46Z | |
| dc.description | Cirelli, Manià and Pizzocchero generalized quantum mechanics by Kähler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative $*$-product as an application. The ordinary quantum mechanics is regarded as a dynamical system of the projective Hilbert space ${\cal P}({\cal H})$ of a Hilbert space ${\cal H}$. The space ${\cal P}({\cal H})$ is an infinite dimensional Kähler manifold of positive constant holomorphic sectional curvature. In general, such dynamical system is constructed for a general Kähler manifold of nonzero constant holomorphic sectional curvature $c$. The Hilbert ball $B_{\cal H}$ is defined by the open unit ball in ${\cal H}$ and it is a Kähler manifold with $c<0$. We introduce the quantum mechanics on $B_{\cal H}$. As an application, we show the structure of the noncommutative function algebra on $B_{\cal H}$. | |
| dc.description | 31 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/funct-an/9710002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9710002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134878 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 81R15; 32Q15 | |
| dc.title | Quantum Mechanics and Operator algebras on the Hilbert ball | |
| dc.type | text |